Accounting for phase variation is often critical when analyzing functional data.
We refer to [1]} and the references therein for an introduction to the general issue and
a detailed overview of available registration approaches.
Many early approaches focused on the alignment of curves towards given (salient) structures,
i.e., landmark registration [2]}.
More recent proposals mostly perform alignment towards
template functions that are either based on domain knowledge or estimated
based on some measure of centrality, with such estimates often iteratively refined
over the course of the registration procedure.
Warping functions are commonly estimated purely nonparametrically
[3]}, [4]}, as (piecewise) linear functions
[5]}, [6]}, [7]} or in a basis expansion.
Common examples for the latter are the use of (penalized) B-spline
[8]}, [9]} or Fourier [10]} bases
or of warplets [11]}.
